Website owner: James Miller
Website owner: James Miller
MOTIVATION FOR EXTENDING THE CONCEPT OF A VECTOR TO INCLUDE OBJECTS OF AN ARBITRARY NATURE. GENERALIZATION OF THE CONCEPT OF A VECTOR SPACE
If we consider the vectors of regular two and three dimensional space we observe that under the operations of addition and multiplication by numbers they form closed systems -- closed systems that we call groups and subgroups, spaces and subspaces. Each space and subspace has a dimension given by the number of linearly independent vectors required to span it. Not only do linear combinations of vectors of two and three dimensional space separate out into spaces and subspaces in this way but so, too, do vectors of Euclidean n-dimensional space. In Matrix Theory we study vectors of Euclidean n-dimensional space. However, in other areas of mathematical study we also encounter this same phenomenon where “things” of various kinds, under addition and multiplication by numbers, form closed systems, groups and subgroups, spaces and subspaces in the same way as do the vectors of two and three dimensional space. In the study of integral equations, differential equations, polynomials, infinite series and infinite sequences, etc. we encounter the same thing. Because of this it has been found useful to generalize the concept of a vector to include “objects” of an arbitrary nature (for which addition and multiplication by a number make sense) and to generalize the entire concept of a vector space, putting it on an axiomatic foundation, separating it from its tie to Euclidean n-dimensional space.
The Way of Truth and Life
God's message to the world
Jesus Christ and His Teachings
Words of Wisdom
Way of enlightenment, wisdom, and understanding
Way of true Christianity
America, a corrupt, depraved, shameless country
On integrity and the lack of it
The test of a person's Christianity is what he is
Who will go to heaven?
The superior person
On faith and works
Ninety five percent of the problems that most people have come from personal foolishness
Liberalism, socialism and the modern welfare state
The desire to harm, a motivation for conduct
The teaching is:
On modern intellectualism
On Self-sufficient Country Living, Homesteading
Principles for Living Life
Topically Arranged Proverbs, Precepts, Quotations. Common Sayings. Poor Richard's Almanac.
America has lost her way
The really big sins
Theory on the Formation of Character
You are what you eat
People are like radio tuners --- they pick out and listen to one wavelength and ignore the rest
Cause of Character Traits --- According to Aristotle
These things go together
We are what we eat --- living under the discipline of a diet
Avoiding problems and trouble in life
Role of habit in formation of character
The True Christian
What is true Christianity?
Personal attributes of the true Christian
What determines a person's character?
Love of God and love of virtue are closely united
Walking a solitary road
Intellectual disparities among people and the power in good habits
Tools of Satan. Tactics and Tricks used by the Devil.
On responding to wrongs
Real Christian Faith
The Natural Way -- The Unnatural Way
Wisdom, Reason and Virtue are closely related
Knowledge is one thing, wisdom is another
My views on Christianity in America
The most important thing in life is understanding
Sizing up people
We are all examples --- for good or for bad
Television --- spiritual poison
The Prime Mover that decides "What We Are"
Where do our outlooks, attitudes and values come from?
Sin is serious business. The punishment for it is real. Hell is real.
Self-imposed discipline and regimentation
Achieving happiness in life --- a matter of the right strategies
Self-control, self-restraint, self-discipline basic to so much in life
We are our habits
What creates moral character?